All Answers 358490 Answers

The exponential operation is always done first.

So its   3^4    .....and then, multiply this answer by 30.

You can use the change of base rule to calculate this....example........

log₆ 19   =  log 19 / log 6

In general

log_a b =   log b / log a

The first two seem ok (as far as I can see, though I can't see the final expression exactly!).

For the third one:

$$y=5\sqrt{x}-x^{-3/2}+\pi^{3/4}$$

$$\frac{dy}{dx}=\frac{5}{2\sqrt{x}}+\frac{3}{2x^{5/2}}$$

$$\frac{dy}{dx}=\frac{1}{2\sqrt{x}}(5+\frac{3}{x^2})$$

.

$$f(x,p)=2(x+4)(x-2p)$$

Differentiate with respect to x

$$\frac{df(x,p)}{dx}=4x-4p+8$$

Set this equal to zero to find the value of x in terms of p at the minimum

$$4x-4p+8=0 \Rightarrow x=p-2$$

Put this value of x back into the f(x,p), set the result equal to -18 and solve for p

$$2(p-2+4)(p-2-2p)=-18$$

$$(p+2)^2=9$$

$$p+2=\pm3$$

so p = 1 and p = -5

.

Very nice, geno.......I wasn't thinking about complex numbers when I did mine, but clearly, that was the intention...!!!!!

^^^^^^ ? ? 

Thanks, geno.....another way to see this is that the sides are just multiples of a 6 -8 -10 Pythagorean Right Triangle.

Thus   9(6, 8, 10)   = 54 - 72 - 90      where 72 is the missing side we want

Anyone Here?

Hi Robtre,

If you want to say something polite and appropriate you can put it on the forum or you can private message the person concerned.

or

3.141592653589793238462643383279502884197169399375105820974944592

that.

x + y  =  11

Since y = 2x, replace the y-term with 2x to get:

 x + 2x  =  11

    3x  =  11

Divide both sides by 3:

    x  =  11/3

Since y = 2x,  y = 2(11/3)  =  22/3

If the side of a square is  s , then the area of theat square is:  Area  =  s².

If the area is 81:    81  =  s²

Finding the square root of both sides,  s  =  9   (Also, -9, but that's impossible.)

Teh perimeter is the distance around the outside, if each side = 9 cm, then all four sides together total 36 cm.

f(x)  = -4x² + 9x + 7

Since  f(x)  =  0,     -4x² + 9x + 7  =  0

Solving by the quadratic formula:    a = -4,  b = 9,   and   c = 7

      x  =  (-9 ± √[ 9² - 4(-4)(7) ] ) / ( 2(-4) )

     x  =  ( -9 ± √[ 193] ) / ( -8 )  

     x  =  2.862  or  -0.6116

Using that formula:     A = 2000          P = 1000         r = 0.06         n= 1         Solve for t.

2000  =  1000(1 + 0.06/1)^(1·t)

2000  =  1000(1.06)^t

Divide by 1000:

2  =  (1.06)^t

If the variable is an exponent, use logs:

log(2)  =  log( 1.06^t )

An exponent in a log comes out as a multiplier:

log(2)  =  t·log(1.06

Divide both sides by log(1.06):

log(2) / log(1.06)  =  t

t  =  11.9  years    (approximately)

When you divide by a number, the greatest number of digits that it can have is 1 fewer than the number that you are dividing by.

For instance,  4/7  =  .571428 571428 571428 ...  (I added the spaces so that the number is easier to read.)

Notice that when dividing by 7, a block of 6 digits repeats. 

(Some fractions don't repeat, like 1/2 = 0.5, and other fractions, like 2/3 = 0.6666 repeat a bock shorter than the number that was used for division -- only one digit repeats, but the number ws divided by 3.)

So  1/17  can have a block of, at most, 16 digits repeating.

1/17  = .05 88 23 52 94 11 76 47 05 88 23 ...  (I used the calculator on this site to get these digits.)

It's up to you to keep the pattern going for 30 places.

From Elizabeth (point A) to the point directly below the kite (pointC) and, from there up to the kite (point B) forms a right griangle with a right angle at C.

Using the Pythagorean Theorem:   c²  =  a² + b²

The distance from A to B is the hypotenuse, c:  c = 90.

The distance From A to C is one of the sides, b:  b = 54

The distance from C to B is the other side, a, the unknown.

c²  =  a² + b²     --->     90²  =  a² + 54²     --->     8100  =  a² + 2916     --->     5184  =  a²

--->   a  =  √5184     --->  a  =  72 ft

The area of a circle if found by multiplyint pi times the value of the radius squared:

A  =  π·r²

The Pythagorean Theorem applies to right triangles:  c²  =  a² + b²

where  c  is the length of the hypotenuse, and  a  and  b  are the lengths of the other two sides.

The problem says that  c = 9  and  a = 6. You are to find the value of  b.

 c²  =  a² + b²     --->      9²  =  6² + b²     --->     81  =  36 + b²     --->     45  =  b²

--->     b  =  √45     --->     b  =  √9√5     --->     b  =  3√5

60000

If the problem is   ln(20164 + 9) / 2   the answer is  4.956...

If that isn't the problem, what is the problem?

What did you try?

Exactly, what did you enter?

(x³)²  =  (x³)·(x³)  =  (x·x·x)·(x·x·x)  =  x^6

The fastest way to find the value of an exponent to an exponent is to multiply the two exponents together:  

        3 x 2  =  6.    --->   (x³)²  =  x³·²  =  x^6

60sec *60min*24hrs

=86400

94500 * .035= 3307.50